For each time step, an outer loop (active-set strategy) is
coupled with an inner loop (Newton's method). Starting from the last converged stick/slip/open region partitioning, we iterate with Newton's method until the 2-norm of the non-linear residual (REF ) is reduced by a factor \(10^{-6}\) . At convergence, a consistency check is carried out to verify the active/inactive status of each fracture element. If the initial stick/slip/open region partitioning has to be updated, another inner Newton's loop is performed. At each Newton's iteration, the system (REF ) is solved by a right-preconditioned full GMRES algorithm [1]}, initialized by the zero vector and stopped when the linear residual is reduced by a factor \(10^{-8}\) . Hence, for each entire simulation we consider the total number of iterations needed for the outer active-set strategy, \(N_{\ell }\) , the inner Newton's loop, \(N_N\) , and the preconditioned GMRES method, \(N_G\) . The average GMRES iteration count for a single linear system is denoted by \(\overline{N}_G\) , with \(N_{G,\min }\)  and \(N_{G,\max }\)  the minimum and maximum value, respectively, required during the entire simulation.
